`Quantitative Finance' is defined as the science that uses and applies advanced mathematics to model the financial market. It has become an active topic that merge the theory of several areas: mathematics, statistics, finance, physics and computer science. In the present book a profound analysis of introductory topics is covered in the first part through exercises, for equity, commodity, currency, fixed-income and credit derivatives. Each exercise is comprehensive developed with fine detail. In the second part of the book two complex applications are provided: a multifactor Heath-Jarrow-Morton, and the uncertain volatility model of Avellaneda-Levy-Paras. Algorithms and programming codes are included to the reader for checking the theoretical results and for developing his own models.